Quantum condensates in nuclear matter

Nonrelativistic nuclear matter is considered as a special example of a many-particle system. Quantum statistical methods are applied to treat the formation and dissolution of bound states in dense matter. The formation of quantum condensates is investigated. Special aspects are the transition from Bose-Einstein condensation (BEC) to Bardeen-Cooper-Schrieffer (BCS) pairing as well as the occurrence of quartetting. Consequences for the structure of nuclei are compared with experimental data. Exercises to illustrate the main features of in-medium effects in nuclear matter are given. The text was submitted by the author in English.     

Quark condensate in the nuclear matter

We calculate the quark condensate in the nuclear matter, taking into account the single-pion and two-pion exchanges between nucleons. We find the dependence of the averaged value of the quark operator¯qq on the density of the matterρ. At very low density the nonlinear terms are proportional toρ ² and increase the tendency to restoration of the chiral symmetry. At larger values of density the account of interaction inside the matter slower down the restoration of chiral symmetry compared to the gas approximation law. The leading nonlinear term in Fermi momentum power expansion becomes of the orderρ ^4/3 . The value of the condensate at the saturation value of density is obtained. The role of multinucleon effects is analyzed.     

Quantum condensates in nuclear matter: Problems

In connection with the contribution “Quantum Condensates in Nuclear Matter” some problems are given to become more familiar with the techniques of many-particle physics. The text was submitted by the authors in English. This paper relates to Part 4: “Problems and Solutions” of materials of the Conference “Helmholtz International Summer School (HISS) on Dense Matter in Heavy-Ion Collisions and Astrophysics,” Dubna, August, 21–September 1, 2006, which were published in the issue 7, 2008.     

Quark condensates in non-Abelian fields at finite temperature

The properties of quark condensates in static non-Abelian fields of the chromomagnetic types are investigated. The dependence of the condensate on the field strength and the temperature is discussed. It is shown that the principal term of the asymptotic expansion for all the investigated field types has the form v^–2 in the high-temperature limit. An expansion is obtained for the quantity in the limit of an arbitrary, uniform, weak field for T=0 and at finite temperature.M. V. Lomonosov State University, Moscow. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 39–52, January, 1994.     

Quark and gluon condensates in a magnetic field

The two-loop expression for the vacuum energy density in a constant magnetic field is obtained on the basis of the chiral perturbation theory. The dependence of the quark and gluon condensates on the field intensity H is found. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 11, 711–717 (10 December 1999)     

Quark confinement in disordered vacuum

We prove quark confinement for a supersymmetric model of disordered QCD.     

Quark matter nucleation in hot hadronic matter

We study the quark deconfinement phase transition in hot β-stable hadronic matter. Assuming a first order phase transition, we calculate the enthalpy per baryon of the hadron–quark phase transition. We calculate and compare the nucleation rate and the nucleation time due to thermal and quantum nucleation mechanisms. We compute the crossover temperature above which thermal nucleation dominates the finite temperature quantum nucleation mechanism. We next discuss the consequences for the physics of proto-neutron stars. We introduce the concept of limiting conversion temperature and critical mass M_cr for proto-hadronic stars, and we show that proto-hadronic stars with a mass M<M_cr could survive the early stages of their evolution without decaying to a quark star.     

Dimension-2 condensates and Polyakov Chiral Quark Models

We address a possible relation between the expectation value of the Polyakov loop in pure gluodynamics and full QCD based on Polyakov Chiral Quark Models where constituent quarks and the Polyakov loop are coupled in a minimal way. To this end, we use a center symmetry-breaking Gaussian model for the Polyakov loop distribution which accurately reproduces gluodynamics data above the phase transition in terms of dimension-2 gluon condensate. The role played by the quantum and local nature of the Polyakov loop is emphasized.     

Quark matter in astrophysics and cosmology

We discuss the role of quark matter in astrophysics and cosmology. The implications of the dynamics of the quark-hadron phase transition in the early universe for the element abundances from big gang nucleosynthesis and the composition of the dark matter in the universe are addressed. We discuss the possibility of deciding on an equation of state for high density matter by observing the cooling of a neutron star remnant of SN1987A. Quark matter models for the Centauros events, Cygnus X-3 cosmic ray events, high energy gamma-ray bursts and the solar neutrino problem are described.     

Quark distributions in nuclei and nuclear effects on nucleon structure functions

Extended quark distribution functions are presented obtained by fitting a large amount of experi-mental data of the ι-A DIS process on the basis of an improved nuclear density model. The experimental data of ι-A DIS processes with A≥ 3 in the region 0.0010 ≤ x ≤ 0.9500 are quite satisfactorily described by using the extended formulae. Our knowledge of the influence of nuclear matter on the quark distributions is deepened.     

Quark distributions in nuclei and nuclear effects on nucleon structure functions

Extended quark distribution functions are presented obtained by fitting a large amount of experimental data of the l-A DIS process on the basis of an improved nuclear density model. The experimental data of l-A DIS processes with A≥3 in the region 0.0010≤x≤0.9500 are quite satisfactorily described by using the extended formulae. Our knowledge of the influence of nuclear matter on the quark distributions is deepened.     

Quark matter equation of state with Hartree-Fock approximation

Both the MIT bag model and potential models are able to reproduce with reasonable accuracy static hadron properties. However while extending the MIT bag model to compute the quark matter equation of state is straightforward, this is not so for potential models. Here this is attempted, starting from a Dirac equation in the Hartree-Fock approximation.     

Quark matter and non-extensive thermodynamics

We investigate different ways of describing the thermodynamics of prehadronic matter in high-energy heavy-ion collisions. The non-extensive thermodynamics with certain assumptions enables an agreement between two important experimental facts. That cannot be achieved using the conventional Gibbs statistics. A massless quark-gluon plasma with E/N=1 GeV energy per particle and T=175 MeV spectral slope temperature can be assumed.     

Quark matter equation of state with Hartree-Fock approximation

Both the MIT bag model and potential models are able to reproduce with reasonable accuracy static hadron properties. However while extending the MIT bag model to compute the quark matter equation of state is straightforward, this is not so for potential models. Here this is attempted, starting from a Dirac equation in the Hartree-Fock approximation.     

Flavour symmetry breaking in quark vacuum condensates

We study SU(3) and SU(2) flavour symmetry violations in the vacuum from the viewpoint of nonperturbative quark mass generation and independently from charge symmetry-breaking considerations. The results for the ratios of quark condensates of different flavours are compatible with those of QCD sum rules. However, we find that very large SU(3) violating effects, suggested by some sum rule analyses, are barely accommodated in the present nonperturbative approach.     

Hall effect in heterogeneous Fe-Ni vacuum condensates

The temperature dependence of the electric conductivity and the Hall and Nernst-Ettinghausen effects of amorphous and microcrystalline Fe-Ni films obtained by ion-plasma sputtering, with a content of technological impurities of about 3 at. %, was studied for the first time. The relationship R_a(T) a²(T), was found between the anomalous Hall constant R_a and . R_a was found to be more sensitive to peculiarities of the complex transformation amorphous, microheterogeneous-crystalline state.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 29–33, September, 1990.